Quantum phase transition of fracton topological orders

Abstract

Fracton topological order (FTO) is a new classification of correlated phases in three spatial dimensions with topological ground state degeneracy (GSD) scaling up with system size, and fractional excitations which are immobile or have restricted mobility. With the topological origin of GSD, FTO is immune to local perturbations, whereas a strong enough global external perturbation is expected to break the order. The critical point of the topological transition is however very challenging to identify. In this work, we propose to characterize quantum phase transition of the type-I FTOs induced by external terms and develop a theory to study analytically the critical point of the transition. In particular, for the external perturbation term creating lineon-type excitations, we predict a generic formula for the critical point of the quantum phase transition, characterized by the breaking-down of GSD. This theory applies to a board class of FTOs, including X-cube model, and for more generic FTO models under perturbations creating two-dimensional (2D) or 3D excitations, we predict the upper and lower limits of the critical point. Our work makes a step in characterizing analytically the quantum phase transition of generic fracton orders.

11 pages + 17 pages Supplementary Material. Important updates have been made for the exact results of critical points

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• Topological Computation without Braiding
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Cited by in corpus (6)

• Fractonic superfluids. (II). Condensing subdimensional particles
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Topological fracton quantum phase transitions by tuning exact tensor network states
• Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
• Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
• Foliated order parameter in a fracton phase transition